Transition times and stochastic resonance for multidimensional diffusions with time periodic drift: A large deviations approach

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dc.creatorHerrmann, Samuel
dc.creatorImkeller, Peter
dc.creatorPeithmann, Dierk
dc.date2004-11-17
dc.date2007-02-09
dc.date.accessioned2026-07-07T07:45:33Z
dc.date.available2026-07-07T07:45:33Z
dc.descriptionWe consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of intensity $ε$, and, therefore, are mathematically described as weakly time inhomogeneous diffusion processes. A system is in stochastic resonance, provided the small noisy perturbation is tuned in such a way that its random trajectories follow the exterior periodic motion in an optimal fashion, that is, for some optimal intensity $ε(T)$. The physicists' favorite, measures of quality of periodic tuning--and thus stochastic resonance--such as spectral power amplification or signal-to-noise ratio, have proven to be defective. They are not robust w.r.t. effective model reduction, that is, for the passage to a simplified finite state Markov chain model reducing the dynamics to a pure jumping between the meta-stable states of the original system. An entirely probabilistic notion of stochastic resonance based on the transition dynamics between the domains of attraction of the meta-stable states--and thus failing to suffer from this robustness defect--was proposed before in the context of one-dimensional diffusions. It is investigated for higher-dimensional systems here, by using extensions and refinements of the Freidlin--Wentzell theory of large deviations for time homogeneous diffusions. Large deviations principles developed for weakly time inhomogeneous diffusions prove to be key tools for a treatment of the problem of diffusion exit from a domain and thus for the approach of stochastic resonance via transition probabilities between meta-stable sets.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051606000000385 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0411386
dc.identifierhttp://arxiv.org/abs/math/0411386
dc.identifierAnnals of Applied Probability 2006, Vol. 16, No. 4, 1851-1892
dc.identifierdoi:10.1214/105051606000000385
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123563
dc.subjectProbability
dc.subject60H10, 60J60, 60F10 (Primary) 60J70, 86A10, 34D45 (Secondary)
dc.titleTransition times and stochastic resonance for multidimensional diffusions with time periodic drift: A large deviations approach
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